In the aim to get high quality graphene films, with large domains and free from impurities, minimizing also the manufacturing costs, we investigate the graphene grown on copper (Cu) foil by chemical vapor deposition at ambient pressure conditions, by using methane (CH4) as carbon source, diluted in a suitable mixture of argon (Ar) and hydrogen (H2). Several graphene samples were synthesized, for variable exposure times to hydrocarbon precursor, in the range from 1 min to 1 hr. The quality of the graphene films and their structural, morphological, and electronic properties were evaluated by micro‐Raman spectroscopy and other techniques, including, scanning tunneling microscopy, atomic force microscopy, and scanning electronic microscopy. In particular, samples obtained with shorter growth time (less than 10 min) exhibit a non‐uniform coverage of the Cu surface, whereas those synthesized with exposure time between 10 and 30 min show a prevalence of well‐ordered monolayer graphene domains. For longer deposition, the amount of disordered domains increases, as revealed by Raman analysis, and the resulting film shows a nonself‐limiting growth behavior for chemical vapor deposition at atmospheric conditions. In addition, we observed 2 kinds of monolayer graphene, in terms of coupling with the Cu surface, for the samples synthesized between 10 and 30 min. To the best of our knowledge, “coupled” and “decoupled” graphene regions have never been reported at the same time on Cu surface. Furthermore, a Raman statistical analysis has been performed on the G and 2D bands measured in both the kinds of regions, gaining evidence of a bimodal behavior for the graphene spots, corresponding to “coupled” and “decoupled” configurations. This difference, which is appreciable also by the optical microscopy inspection, could be related to the local Cu oxidation and to oxygen intercalation after graphene growth.